standard deviation for harmonic mean

hvar.py

from scipy.stats import hmean 


# https://stats.stackexchange.com/questions/7471/can-the-standard-deviation-be-calculated-for-harmonic-mean
harmonic_var = lambda S : (np.power(S,-1).var())/(len(S)*np.power(np.power(S,-1).mean(),4))

# example
import numpy as np
np.random.seed(100)
s = np.random.dirichlet((1,5),10)
S = s.T[1]
print("S: ", S)
print("harmonic variance S: ", harmonic_var(S))
"""
>>> S:  [0.81934176 0.99756006 0.79016822 0.69804071 0.95343128 0.70649118 0.68389881 0.53041986 0.9714669  0.78779674]
>>> harmonic variance S:  0.0021948755349154346
"""